Relations Between Variously Defined Effects and Interactions in Analysis of Variance

Abstract

From an algebraic point of view the analysis of variance tests of effects and interactions can be based on the minimum values of a certain quadratic expression in which the "$h$-matrix" (defined in Section 3) is fundamental. The arbitrariness in the choice of this matrix reflects the arbitrariness in the definition of effects and interactions. The paper considers the dependence of the result of these tests on the $h$-matrix used and expresses the answer by the two theorems of Section 4, which are proved in the subsequent sections.